PPT-Graph Algorithms Counting Triangles

Transitive Closure Jeffrey D Ullman Stanford University Infolab Counting Triangles Bounds on Numbers of Triangles Heavy Hitters An Optimal Algorithm Counting Triangles Why Care Density of triangles measures maturity of a community. Lecture 18. The basics of graphs.. 8/25/2009. 1. ALG0183 Algorithms & Data Structures by Dr Andy Brooks. Watch out for self-loops in graphs.. 8/25/2009. ALG0183 Algorithms & Data Structures by Dr Andy Brooks. 1. Graph Algorithms. Many problems are naturally represented as graphs. Networks, Maps, Possible paths, Resource Flow, etc.. Ch. 3 focuses on algorithms to find connectivity in graphs. Ch. 4 focuses on algorithms to find paths within graphs. . Charalampos (Babis) E. Tsourakakis. ctsourak@math.cmu.edu. WAW 2010, Stanford. . 16. th. December ‘10. WAW '10. 1. Joint work . Richard Peng. SCS, CMU. Gary L. Miller . George Caragea, and Uzi Vishkin. University of Maryland. 1. Speaker. James Edwards. It has proven to be quite . difficult. to obtain significant performance improvements using current parallel computing platforms.. Reference Counting vs. Tracing. Advantages. Immediate. Object-local. Overhead distributed. Very simple . Trivial implementation for naïve RC. Disadvantages. Maintain count . Time and space overheads. Talya Eden, . Tel Aviv . University. Amit Levi, . University of Waterloo. Dana . Ron, . Tel Aviv . University. C. . Seshadhri. , . UC Santa Cruz. Counting Triangles. Basic graph-theoretic algorithmic . of Large Datasets. . Charalampos (Babis) E. Tsourakakis. Brown University. charalampos_tsourakakis@brown.edu. Brown University. Node Differential . Privacy . Sofya. . Raskhodnikova. Penn State University. Joint work with. . . Shiva . Kasiviswanathan. . (. GE Research. ),. . Kobbi. . Nissim. . (. Ben-Gurion U. and Harvard U.. of Large Datasets. . Charalampos (Babis) E. Tsourakakis. Brown University. charalampos_tsourakakis@brown.edu. Brown University. Talya Eden, . Tel Aviv . University. Amit Levi, . University of Waterloo. Dana . Ron, . Tel Aviv . University. C. . Seshadhri. , . UC Santa Cruz. Counting Triangles. Basic graph-theoretic algorithmic . R. Garcia is supported by an NSF Bridge to the Doctorate Fellowships. .. The biological imaging group is supported by MH-086994, NSF-1039620, and NSF-0964114.. . Abstract. Automating segmentation of individual neurons in electron microscopic (EM) images is a crucial step in the acquisition and analysis of connectomes. It is commonly thought that approaches which use contextual information from distant parts of the image to make local decisions, should be computationally infeasible. Combined with the topological complexity of three-dimensional (3D) space, this belief has been deterring the development of algorithms that work genuinely in 3D. . CIS 606. Spring 2010. Graph representation. Given graph . G. . = (. V. , . E. ). . In . pseudocode. , represent vertex set by . G.V . and edge . set by . G.E. .. G . may be either directed or undirected.. Accurate Triangle Counting in Graph Streams with Deletions. Kijung Shin. , . Jisu. Kim, Bryan . Hooi. , Christos . Faloutsos. Triangles in a Graph. Accurate Triangle Counting in Graph Streams with Deletions. Announcements. Talk on technical interviews . today!. Gugenheim. 220 at 1:10 PM.. Para Exercise feedback soon.. P2 Feedback (hopefully) Saturday.. Announcements. Please fill out course evaluations..